Diffusion in interfaces on surfaces and along dislocations Grain Boundary Diffusion : Diffusion along grain boundaries is more rapid than normal lattice diffusion. Packing density in a grain boundary is less than the perfect lattice so atoms can change places more easily. d

Isotope diffusion experiments indicate that where and When is GB diffusion important? Consider the following model of steady state diffusion: d J GB JLJL d >> : is the GB width ~ 0.5nm Depends upon GB width δ, grain size d and also D GB / D L.

Suppose there are N T atoms per unit time diffusing through a grain of width d with boundary width δ. from Fick’s 1 st law – assuming steady state

or So obviously Grain boundary diffusion is important for Now recall So that Defining an apparent diffusion coefficient

Typically DLDL D GB (δ/d) D app At low temperature there is an important contribution of D GB to the flux. The cross-over occurs at ~ 0.75 T mp. and D GB 1 / T log D

=> Dislocation –core diffusion often referred to as “pipeline diffusion” Dislocation JLJL JpJp following a procedure similar to the gb case Diffusion along Dislocations

Here g is the sum of the pipe cross-sectional areas per unit area of matrix. For example the core radius is ~ cm and a well-annealed metal contains as 10 6 disl / cm 2 so: Dislocation effects can become important below as 0.5 T mp.

at high temp D s is dominated by adatom migration at low temp D s is dominated by surface vacancy migration Surface Diffusion Terrace-ledge-kink surface Adatom Ledge adtom Terrace vacancy kink

} } Adatom equil. Pop. Surf vac. equil. Pop. N o is the # of terrace sites per unit area. For metals N o ~ cm 2.

where and The total surface flux contains contributions from vacancies and ad-atoms. :

Scratch smoothening Curved arrows indicates mass - flow Most measurements have involved so-called mass transfer methods. D a has been measured for tungsten using for FIM Measurement of D s : W d Sinusoidal profile decay A(t)

W Grain boundary grooving Assume the surface has one principal curvature. Assuming  is the isotropic. where  is the curvature. v m is the molar volume.

A positively curved surface has a higher chemical potential than either a flat or a negatively curved surface so mass will flows along surface from the hills to the valleys. W Grain Boundary Grooving Sinusoidal profile decay A(t)

Protrusions build up with field on and decay exponentially with field off. A(t) Field Emission Tip